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Ch15

2.
Learning Objectives <ul><li>Analyze and interpret nonlinear variables in multiple regression analysis. </li></ul><ul><li>Understand the role of qualitative variables and how to use them in multiple regression analysis. </li></ul><ul><li>Learn how to build and evaluate multiple regression models. </li></ul><ul><li>Learn how to detect influential observations in regression analysis. </li></ul>

4.
Non Linear Models: Mathematical Transformation First-order with Two Independent Variables Second-order with One Independent Variable Second-order with an Interaction Term Second-order with Two Independent Variables

20.
Indicator (Dummy) Variables <ul><li>Qualitative (categorical) Variables </li></ul><ul><li>The number of dummy variables needed for a qualitative variable is the number of categories less one. [c - 1, where c is the number of categories] </li></ul><ul><li>For dichotomous variables, such as gender, only one dummy variable is needed. There are two categories (female and male); c = 2; c - 1 = 1. </li></ul><ul><li>Your office is located in which region of the country? ___Northeast ___Midwest ___South ___West number of dummy variables = c - 1 = 4 - 1 = 3 </li></ul>

27.
Stepwise Regression <ul><li>Perform k simple regressions; and select the best as the initial model </li></ul><ul><li>Evaluate each variable not in the model </li></ul><ul><ul><li>If none meet the criterion, stop </li></ul></ul><ul><ul><li>Add the best variable to the model; reevaluate previous variables, and drop any which are not significant </li></ul></ul><ul><li>Return to previous step </li></ul>

32.
Multicollinearity <ul><li>Condition that occurs when two or more of the independent variables of a multiple regression model are highly correlated </li></ul><ul><ul><li>Difficult to interpret the estimates of the regression coefficients </li></ul></ul><ul><ul><li>Inordinately small t values for the regression coefficients </li></ul></ul><ul><ul><li>Standard deviations of regression coefficients are overestimated </li></ul></ul><ul><ul><li>Sign of predictor variable’s coefficient opposite of what expected </li></ul></ul>